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Einstein came along and discovered
that these non-Euclidean geometries were just the thing to describe
the real-world interactions of objects with mass - that is, to
describe gravity. examples on math forum; This is a case where the mathematical system was
invented with no consideration of the real world (and therefore no
faith element), but it turned out that this system does appear to
describe the real world.
The experiments to show that Einstein's theory of general relativity
do describe the real world better than any other mathematical system
are very tricky; it is still possible that another system would do
better. We can be absolutely sure that the results of general
relativity theory follow from its assumptions; the only question is
whether or not those assumptions match the way the real world is.
more examples on online math forum.
Einstein came along and discovered
that these non-Euclidean geometries were just the thing to describe
the real-world interactions of objects with mass - that is, to
describe gravity. examples on math forum; This is a case where the mathematical system was
invented with no consideration of the real world (and therefore no
faith element), but it turned out that this system does appear to
describe the real world.
The experiments to show that Einstein's theory of general relativity
do describe the real world better than any other mathematical system
are very tricky; it is still possible that another system would do
better. We can be absolutely sure that the results of general
relativity theory follow from its assumptions; the only question is
whether or not those assumptions match the way the real world is.
more examples on online math forum.
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